Non-parametric Fisher’s discriminant analysis with kernels for data classification

Kernel mapping has attracted a great deal of attention from researchers in the field of pattern recognition and statistical machine learning. Kernel-based approaches are the better choice whenever a non-linear classification model is needed. This paper proposes a nonlinear classification approach based on the non-parametric version of Fisher’s discriminant analysis. This technique can efficiently find a nonparametric kernel representation where linear discriminants perform better. Data classification is achieved by integrating the linear version of the nonparametric Fisher’s discriminant analysis with the kernel mapping. Based on the kernel trick, we provide a new formulation for Fisher’s criterion, defined solely in terms of the inner dot-product of the original input data. The obtained experimental results have demonstrated the competitiveness of our approach compared to major state of the art approaches.

► We propose a new supervised kernel-based classification approach that behaves nonlinearly.
► It defines a non-linear generalization of the NDA technique to perform in kernel feature space.
► It relaxes the normality assumption of FDA using the non-parametric form of the SB scatter matrix.
► We provide a new formulation for the main criterion defined solely in terms of the Gram matrix K.
► The obtained experimental results have demonstrated the efficiency of our approach.